Reliability estimation of a multicomponent stress‐strength model for unit Gompertz distribution under progressive Type II censoring
Mayank Kumar Jha, Sanku Dey, Refah Alotaibi, Yogesh Mani Tripathi
Abstract
Abstract We consider the problem of estimating multicomponent stress‐strength (MSS) reliability under progressive Type II censoring when stress and strength variables follow unit Gompertz distributions with common scale parameter. We estimate MSS reliability under frequentist and Bayesian approaches. Bayes estimates are obtained by using Lindley approximation and Metropolis‐Hastings algorithm methods. Further, we obtain uniformly minimum variance unbiased estimates of the reliability when common scale parameter is known. Asymptotic, bootstrap confidence interval and highest posterior density credible intervals have been constructed. We perform Monte Carlo simulations to compare the performance of proposed estimates and also present a discussion. Finally, three real data sets are analyzed for illustrative purposes.